High power fiber amplifiers have been the subject of intensive research and development for applications such as material processing and defense. Amplification of single frequency radiation (e.g., laser linewidths less than 100 MHz) is required for specific applications, such as coherent combination of multiple apertures for power scaling and large scale interferometeric measurement techniques such as gravity wave detection.
Fiber-based optical amplifiers offer several advantages relative to conventional solid-state lasers in these applications, such as better conversion efficiencies, ease in thermal management, broadband gain and good transverse mode stability. However, the relatively long interaction length L required by optical fiber amplifiers imposes significant nonlinear limitations to achieving maximum optical power. The most severe nonlinear limit for single frequency amplifiers is stimulated Brillouin scattering (SBS).
SBS is an inherent effect that occurs in fiber amplifiers in which the forward-propagating power in the amplifier is converted into backward-propagating power with a slightly downward frequency shift that limits the power transfer through the amplifier. The backward propagating Stokes wave essentially robs power from the desired, forward propagating signal so as to limit the power of the optical signals that can be transmitted via the optical fiber. With reference to quantum physics, SBS can therefore be described by the transfer of a photon from the optical wave into a new Stokes photon of lower frequency and the creation of a new phonon that adds to the acoustic wave. Even though the Stokes power is low at the source of the Stokes wave in an optical amplifier, the backward-propagating Stokes light undergoes ionic gain, competing with the desired “forward” gain of the propagating signal and, as a result, clamping the output power of the amplifier. Other detrimental optical noise signals typically occurring in fiber lasers and amplifiers can have the similar effect of experiencing ionic gain (and thus further limiting the available output power in the amplifier). For example, unwanted Raman scattering may overlap with the broad gain bandwidth of various types of gain medium, thus also experiencing ionic gain. Additionally, unwanted optical modes can experience ionic gain when they spatially overlap the gain-doped region of the fiber core. Clearly, ionic gain is problematic and techniques that achieve selective ionic gain for the desired optical mode of interest while reducing (or eliminating) ionic gain in the unwanted modes (defined as “noise” in this context) is highly desirable.
One recent approach to increasing the power threshold associated with the onset of SBS in fiber amplifiers involves the use of higher-order mode (HOM) optical fibers. The power threshold for SBS in passive optical fibers is frequently cited as:
                                          P            th                    =                                    21              ⁢                              A                eff                                                                    g                B                            ⁢                              L                eff                                                    ,                            (        1        )            where Aeff is the effective area of the optical core region, gB is the Brillouin gain coefficient and Leff is the effective interaction length of the optical fiber amplifier. The effective interaction length is defined as follows:
                              L          eff                =                              1            -                          ⅇ                                                -                  α                                ⁢                                                                  ⁢                L                                              α                                    (        2        )            where α is the optical attenuation coefficient in units of inverse meters and L is the physical length of the fiber. Further, the optical effective area Aeff for a radially-symmetric optical mode can be defined as follows:
                                          A            eff                    =                                                    〈                                                      f                    ⁡                                          (                      r                      )                                                        2                                〉                            r              2                                                      〈                                                      f                    ⁡                                          (                      r                      )                                                        4                                〉                            r                                      ,                            (        3        )            where f(r) is the electric field distribution of the propagating optical mode and < . . . >, represents the integral over the defined fiber cross section.
It is well-known that an optical fiber designed to support the propagation of higher-order modes (such as, for example, the LP08 mode) exhibits a larger optical effective area Aeff than fibers used for propagating of fundamental mode (LP01) signals. This larger value of Aeff leads to an increase in the SBS power threshold (see equation (1)). Indeed, an HOM fiber designed to propagate the LP08 mode may have an effective area of approximately 1800 μm2, compared to a more conventional large mode area (LMA) fiber supporting the propagation of the fundamental LP01 mode with an effective area of approximately 300 μm2. Other optical effects that impose limits due to high optical intensity, such as the nonlinear mechanisms of stimulated Raman scattering, self-phase modulation, cross-phase modulation, modulation instability, and the like, similarly benefit from the larger Aeff of HOM fiber.
While, in theory, the utilization of higher-order modes (and the associated larger effective area) should provide a significant improvement over the use of lower-order mode (LOM) signals in a fiber amplifier, the actual power thresholds associated with the use of HOMs have not been found to be as high as expected.